Incremental Elasticity of Pre-stretched Elastomers with Strain Hardening Effect: Half-Space and Thin-Layer Limits
摘要
Soft materials, such as rubber, biological tissues, and hydrogels, typically exhibit strain hardening effect that preserves their structural integrity and function. Moreover, these materials are rarely stress- or strain-free in their natural or engineered states. The presence of pre-stress and pre-strain significantly influences their mechanical properties. In this paper, we investigate the mechanical response of pre-stretched, strain hardening soft elastomers in two limiting cases: the half-space and the thin layer. By employing the Fourier transform, we derive the surface Green’s function for the half-space. A perturbation approach is utilized to obtain an analytical expression for the surface deformation of a pre-stretched thin layer bonded to a rigid substrate. Based on these derivations, spherical indentation problems for both limiting configurations are analyzed. The relationship between indentation force and indentation displacement is influenced by the pre-stretch state and the number of chain segments of the elastomer, i.e., the hardening parameter. The theoretical results are consistent with finite element simulations. Overall, this study provides a versatile theoretical basis for characterizing the mechanical properties and analyzing other surface phenomena of pre-stretched soft materials with strain hardening effect.